Sliding mode formation control method for double-layer heterogeneous multi-agent system

Abstract

The invention belongs to the technical field of multi-agent systems, and particularly relates to a double-layer heterogeneous multi-agent system sliding mode formation control method, which comprises the steps of S1, constructing a double-layer heterogeneous multi-agent system according to a preset form; s2, setting a cross-level hybrid communication topological structure for the double-layer heterogeneous multi-agent system; s3, setting a system control rate of the double-layer heterogeneous multi-agent system; and S4, based on the constructed double-layer heterogeneous multi-agent system, performing formation control and obstacle avoidance cooperative operation of the multi-agent system by using the system control rate in the S3, and ensuring that the system realizes cooperative consistency of reference tracking errors and real-time prevention and control of collision risks under the condition that mismatching uncertainty exists. According to the method, the coordination consistency of tracking errors and real-time prevention and control of collision risks can be ensured while the uncertainties of mismatching are processed.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of multi-agent systems, and particularly relates to a double-layer heterogeneous multi-agent system sliding mode formation control method. BACKGROUND

[0002] In recent years, as an important research direction of complex system modeling and collaborative control, multi-agent systems (MAS) have attracted widespread attention from academia and industry. With the rapid development of artificial intelligence, sensor technology and communication networks, multi-agent systems are increasingly widely used in fields such as network consensus and security protection, traffic signal optimization, robot group collaboration, search and rescue, swarm control, and energy trading. Among them, double-layer heterogeneous multi-agent systems have gradually become a research hotspot due to their significant advantages in information processing efficiency, task division flexibility, and system scalability. For example, existing literature has proposed a heterogeneous group control method based on a double-layer communication topology, which realizes efficient management of large-scale systems through a hierarchical architecture.

[0003] In a typical double-layer structure, the system usually contains a high-level agent (i.e., "leader") and multiple low-level agents (i.e., "follower"). The high-level agent is responsible for environmental perception, global decision-making, and task scheduling, while the low-level agents focus on executing specific actions such as path tracking, obstacle avoidance navigation, etc. This leader-follower architecture not only realizes centralized processing and decentralized execution of information, but also improves the overall response speed and robustness of the system. Especially in dynamic and uncertain environments, the high-level agent can integrate information from multiple low-level nodes, make global optimization decisions, and issue instructions to the bottom execution unit through a reasonable communication mechanism, thereby ensuring the consistency and stability of the entire system operation.

[0004] However, in actual application scenarios, multi-agent systems face many challenges. First, with the increase in the number of agents and the complexity of tasks, there are a large number of dynamic interactions and spatial couplings within the system, leading to a significant increase in collision risk. Especially in high-density operation scenarios (such as unmanned aerial vehicle formation flight, autonomous vehicle fleet), if there is a lack of effective collision warning and avoidance mechanism, it is easy to cause a chain reaction, affecting the task completion rate and even causing physical damage. Therefore, how to accurately assess and prevent collision risks in real time has become one of the key problems in the safety design of multi-agent systems.

[0005] Secondly, the system often faces the influence of model uncertainty, external disturbance, communication delay and sensor noise in the process of running, which will destroy the cooperative consistency of the formation. Therefore, robust formation control becomes the research focus. The ideal formation control should have good anti-interference ability and be able to maintain the stability of the target formation and the accuracy of trajectory tracking under the condition of parameter perturbation or environmental change. Traditional linear control methods often have difficulty in dealing with such strong nonlinear and time-varying systems, and it is urgent to introduce more adaptive control strategies.

[0006] Under this background, sliding mode control (SMC) is widely used in the cooperative control of multi-agent systems due to its strong robustness to system uncertainty and external disturbance. Sliding mode control constructs a sliding surface and designs a switching function, so that the system state reaches and remains on the sliding surface in a limited time, thereby achieving accurate tracking of the desired behavior. Existing research shows that sliding mode control has superior performance in dealing with time delay, nonlinear interaction and parameter uncertainty, and is especially suitable for formation and coordination tasks of heterogeneous multi-agent systems. By designing an adaptive sliding mode controller, the stability and convergence speed of the system can be enhanced, and the adverse effects of external disturbances can be effectively suppressed.

[0007] Although the above research has made some progress, there are still several key problems that have not been solved in the double-layer heterogeneous multi-agent system. On the one hand, most existing methods assume a single communication topology or a fixed information flow mode between the upper and lower levels, and do not fully consider the timeliness and integrity of cross-level information fusion. Especially in the process of high-level agents needing to process perception data from multiple low-level followers and quickly feedback to the bottom execution unit, if there is no efficient hybrid communication structure support, it is easy to cause information delay, misjudgment or response lag, and thus affect the overall coordination efficiency. On the other hand, most current sliding mode control schemes only focus on the coordination between single or multi-homogeneous agents, and lack systematic modeling of the dynamic matching problem between high-level decision and low-level execution in the double-layer heterogeneous system, making it difficult to balance global optimization and local safety needs.

[0008] In addition, existing anti-collision mechanisms mostly rely on local distance detection or simple potential field methods, lacking comprehensive judgment ability for global environment situation, and being difficult to adapt to real-time obstacle avoidance requirements in complex dynamic scenarios. Under the high-level-low-level cooperative framework, how to embed the anti-collision logic into the sliding mode control law to realize the unified optimization of formation consistency and collision risk prevention is still a technical difficulty. Due to the high dimensionality of system state, complex coupling relationship, and involvement of nonlinear dynamics and uncertain disturbances, designing a compound control strategy that can guarantee both formation stability and real-time collision avoidance is extremely challenging in terms of theoretical analysis and engineering implementation.

[0009] Therefore, how to construct a sliding mode formation control method with efficient information interaction, strong robustness and real-time collision avoidance capability in a double-layer heterogeneous multi-agent system to realize the cooperative consistency of tracking error and real-time prevention and control of collision risk under the condition of unmatched uncertainty has become a problem to be solved. SUMMARY

[0010] In view of the above problems of the prior art, the present application provides a double-layer heterogeneous multi-agent system sliding mode formation control method, which can ensure the cooperative consistency of tracking error and real-time prevention and control of collision risk while dealing with unmatched uncertainty.

[0011] To solve the above technical problems, the present application adopts the following technical solutions:

[0012] A double-layer heterogeneous multi-agent system sliding mode formation control method, comprising the following steps:

[0013] S1, constructing a double-layer heterogeneous multi-agent system according to a predetermined form; the double-layer heterogeneous multi-agent system comprises two levels of high-level and low-level, and each level of agent comprises one leader and N followers, and the followers of the high-level and the low-level are one-to-one corresponding by index; wherein N≥1;

[0014] S2, setting a cross-level mixed communication topology structure for the double-layer heterogeneous multi-agent system; the cross-level mixed communication topology structure comprises:

[0015] The high-level agent can detect the information around the agent at the corresponding position of the low-level or its adjacent agent;

[0016] Each high-level follower transmits the environmental information obtained through perception detection to the high-level leader; the high-level leader obtains the environmental information by itself exploration and receiving information from each high-level follower;

[0017] The high-level follower can directly transmit the detected information to the corresponding low-level follower to realize fast response;

[0018] The high-level leader transmits the comprehensive obtained environmental information to the low-level leader, and then the low-level leader distributes it to all low-level followers to ensure the overall cooperation of the formation;

[0019] S3, setting the system control rate u of the double-layer heterogeneous multi-agent system i (t)=u 1,i (t)+u 2,i (t); wherein u 1,i (t) is the high-level control rate, u 2,i (t) is the low-level control rate;

[0020] The high-level control rate

[0021] In the formula, I(t) represents the amount of perception information about the low-level environment received by the high-level leader from the corresponding high-level follower; H(t) represents the obstacle signal strength detected by the high-level leader itself; W(t) represents the feedback information strength or amount reflecting the low-level formation coordination state and control demand received by the high-level leader from the low-level leader; k1(t), k2(t), and k3(t) are weight coefficients; is the collision avoidance control rate of the high level;

[0022] is the control rate of the low level

[0023] In the formula, is the collision avoidance control rate of the low level; is a formation coordination controller based on a sliding mode control, used to ensure the relative position stability and trajectory tracking consistency among the low-level intelligent agents;

[0024] S4, based on the constructed double-layer heterogeneous multi-agent system, using the system control rate of S3, the formation control and obstacle avoidance coordination operation of the multi-agent system are carried out, and the reference tracking error consistency and real-time collision risk prevention of the system are ensured under the condition of existing mismatch uncertainty.

[0025] Compared with the prior art, the present application has the following beneficial effects:

[0026] 1. The double-layer heterogeneous multi-agent system structure is constructed, and efficient division of labor of information processing and task execution is realized. The present method proposes a heterogeneous multi-agent system structure containing two levels of high level and low level, each level is provided with one leader (pilot) and N followers (followers), and the followers of the high level and the low level are one-to-one corresponding according to the index. This structure separates global decision and local execution: the high-level agent is responsible for perceiving the environment, integrating information and making macro decision; the low-level agent is focused on path tracking and obstacle avoidance and other specific operations. Compared with the traditional single-layer or multi-homogeneous intelligent agent system, the double-layer structure significantly improves the scalability and task processing efficiency of the system. Especially in large-scale group tasks, the communication overhead and computing bottleneck caused by direct communication of all intelligent agents are avoided, the optimization mode of "centralized decision and distributed execution" is realized, and the organization and controllability of the system are enhanced.

[0027] 2. The cross-layer hybrid communication topology improves the integrity and timeliness of information transmission. The cross-layer hybrid communication topology is introduced, including: the high-level agent can detect the environmental information of the corresponding position or adjacent agent of the bottom layer; the high-level follower uploads the sensing information to the high-level leader; the high-level leader transmits the comprehensive environmental information to the low-level leader; the low-level leader distributes the instructions to each low-level follower; at the same time, the high-level follower can also directly transmit information to the corresponding low-level follower to achieve rapid response. This hybrid communication mechanism breaks through the limitations of the traditional single uplink and downlink communication mode, ensuring the convergence and coordination of global information, and retaining the local rapid response capability. Compared with the existing communication mode which only relies on the central node or fixed topology, this structure effectively alleviates the information delay problem and improves the adaptability and coordination efficiency of the system in a dynamic environment.

[0028] 3. Design a hierarchical composite control law, combining sliding mode control and collision avoidance mechanism. The system control rate is decomposed into high-level control rate u 1,i (t) and low-level control rate u 2,i (t). The high-level control rate is composed of environmental perception information I(t), obstacle signal strength H(t), formation feedback information W(t) and anti-collision term , realizing the "decision-execution-feedback" closed loop. This multi-dimensional integration not only ensures the processing of high-priority tasks, but also dynamically quantifies the risk, providing a comprehensive decision basis for cross-layer collaboration. The low-level control rate is composed of anti-collision control term and the collaborative controller based on sliding mode control , ensuring the position stability and trajectory consistency between low-level agents. This design realizes the closed-loop control logic of "high-level decision-driven + low-level sliding mode execution". Compared with the traditional method of using sliding mode control only in the low layer, this scheme embeds sliding mode control into the entire hierarchical system and optimizes it jointly with the anti-collision logic, enhancing the robustness of the system to uncertainties and improving the overall control accuracy and safety.

[0029] 4. Realize the collaborative operation of formation control and obstacle avoidance, considering consistency and safety. By integrating the anti-collision control term into the high-level and low-level control law, the formation control and collision risk prevention are synchronized. The high-level leader can consider the obstacle distribution and formation state when making decisions, generating safe instructions in advance; the low-level agent can also respond to local threats in real time during execution, avoiding trajectory mutation or formation rupture caused by passive obstacle avoidance. Compared with the existing method of independent processing of formation control and obstacle avoidance (such as completing formation first and then triggering obstacle avoidance), this scheme realizes the integrated design of the two, reducing control conflicts and response delays, and improving the overall performance of the system in complex dynamic environments.

[0030] In summary, the method effectively solves the deficiencies of traditional multi-agent systems in information transmission efficiency, control robustness and safe cooperation by constructing a double-layer heterogeneous architecture, designing a hybrid communication topology, introducing a hierarchical sliding mode control law and integrating a collision avoidance mechanism. It not only improves the stability and adaptability of the system under conditions of model uncertainty, external disturbance and communication mismatch, but also realizes the unified optimization of formation consistency and collision risk prevention and control.

[0031] The method can ensure the cooperative consistency of tracking error and real-time prevention and control of collision risk while handling mismatch uncertainty.

[0032] Preferably, in S3, the low-level collision avoidance control rate is:

[0033]

[0034] where k ij is the weight coefficient; p ij (t) is the switching function; r ij (t) is the control force intensity function; and q ij (t) is the control force direction function.

[0035] Such settings, 1, realize the modularity and adjustability of collision avoidance control, and enhance the flexibility of the system. The collision avoidance control rate is decomposed into four independent functions of weight, switch, intensity and direction, making the control logic clearer and easier to adjust. By adjusting the weight coefficient k ij , the safety and motion smoothness can be balanced in different task scenarios; and the switching function p ij (t) realizes the "on-demand activation" intelligent response mechanism, avoiding unnecessary control intervention. Compared with the traditional fixed threshold or continuous obstacle avoidance strategy, this modular design significantly improves the flexibility and controllability of the system, especially suitable for dynamic environments with frequent changes in task priority.

[0036] 2, support real-time dynamic obstacle avoidance, and improve safety and response speed. Since r ij (t) and q ij (t) are both dynamic functions that change over time, this control law can adaptively adjust the size and direction of the obstacle avoidance force according to real-time perception of obstacle distance, relative speed and other information. This enables low-level agents to respond quickly when collision risks are detected, avoiding collision accidents caused by delays or misjudgments. Compared with obstacle avoidance methods that rely on pre-set paths or global planning, this scheme has stronger local adaptability, especially suitable for multi-agent systems operating in unknown or rapidly changing environments.

[0037] 3. Work with the sliding mode control to ensure the stability of the formation and the consistency of the obstacle avoidance. The anti-collision control term is embedded into the low-level total control rate, and works with the collaborative controller based on the sliding mode control . Since the sliding mode control itself has strong robustness, the coupling of the anti-collision term will not destroy the overall convergence of the system, but can realize safe obstacle avoidance on the premise of ensuring the consistency of trajectory tracking. Compared with the method of separating obstacle avoidance and formation control, the preferred embodiment realizes the collaborative goal of "safe and undisturbed, obstacle avoidance without leaving the team", effectively alleviating the problem of "formation rupture caused by obstacle avoidance" in traditional methods.

[0038] Preferably, in S3, the anti-collision strategy of the high layer adopts the same anti-collision control rate as the low-level agent, and the anti-collision control rate of the high layer is:

[0039]

[0040] Preferably, the control force strength function r ij (t) is:

[0041]

[0042] In the formula, Ω ij is the critical distance, when ||e ij (t)||<Ω ij , it is considered that the agents i and j have entered the collision risk area; is the risk-free boundary parameter; ξ is a preset index for emphasizing the influence degree of the distance on the control force; β ij is the collision risk angle of the agents i and j.

[0043] Such setting, 1. Realize the nonlinear gradual enhancement of the control force strength, and improve the sensitivity and safety of the obstacle avoidance response. The control force strength is designed to be proportional to the power of the reciprocal of the relative distance, and the sigmoid function is introduced for smooth modulation. When the distance between the agents decreases, the control force increases nonlinearly, especially when the critical distance Ω ij is approached, the control force rapidly rises, thereby realizing the obstacle avoidance response mechanism of "the closer, the stronger". Compared with the linear or step-type control force design, this nonlinear structure can more realistically simulate the "sense of urgency" in human driving or biological obstacle avoidance behavior, effectively prevent collision accidents caused by slow response, and significantly improve the safety margin of the system.

[0044] 2. Introduce the collision risk angle β ij for segmented regulation to realize directional obstacle avoidance priority judgment. The control force strength not only depends on the distance, but also is segmented according to the collision risk angle β ij : when β ijwhen β > π / 2 (i.e. approaching trend is head-on or lateral), the control strength is dynamically adjusted according to the distance. This mechanism embodies the "direction-aware" obstacle avoidance logic, avoiding the same strength response to all close contact, thus reducing unnecessary control disturbance and improving the intelligence and rationality of the obstacle avoidance strategy. ij <π / 2, the control strength is dynamically adjusted according to the distance. This mechanism embodies the "direction-aware" obstacle avoidance logic, avoiding the same strength response to all close contact, thus reducing unnecessary control disturbance and improving the intelligence and rationality of the obstacle avoidance strategy.

[0045] 3. The sigmoid function is used to realize smooth transition, ensuring system stability and continuity. By using the sigmoid function to map the risk difference , the control force does not suddenly change when entering the danger zone, but smoothly rises. This helps to avoid sharp oscillation of the control signal, reduces the load of the actuator, and ensures the stability of the closed-loop system. In addition, this design makes the control law mathematically well-differentiable, facilitating subsequent coupling with high-order controllers such as sliding mode control, and improving the convergence and robustness of the overall control performance.

[0046] In summary, this method realizes precise, intelligent and smooth adjustment of obstacle avoidance control force by composite modeling of control force strength function based on distance, risk angle and smooth activation, which not only enhances the safety response capability of the system at close range, but also avoids the instability problem caused by excessive intervention.

[0047] Preferably, the collision risk angle β ij of the intelligent agents i and j is calculated as follows:

[0048]

[0049] wherein, v i (t) and v j (t) are the motion speeds of intelligent agents i and j respectively, and when v j (t) = 0, it can be regarded as a fixed obstacle; α ij is the collision risk angle of intelligent agent i relative to intelligent agent j, defined as the angle between the moving direction of intelligent agent i and the straight line from intelligent agent i to intelligent agent j, and it is stipulated that 0 ≤ α ij ≤ π; α ji is the collision risk angle of intelligent agent j relative to intelligent agent i;

[0050] Based on the size of the collision risk angle β ij , the collision risk level between intelligent agents i and j is divided into the following three levels:

[0051] If β , there is a high collision risk between intelligent agents i and j;

[0052] If β There is low collision risk between agent i and j.

[0053] If There is no collision risk between agent i and j.

[0054] Such a setting, 1. Realize the dynamic quantitative evaluation of collision risk, improve the accuracy of obstacle avoidance decision. Traditional methods often rely only on relative position to determine whether it is close, ignoring the influence of relative motion direction, easy to cause misjudgment (such as far away but close distance is mistaken for dangerous). This method introduces the collision risk angle β ij , considering the speed and direction relationship of two agents, realizing the dynamic, geometric evaluation of collision possibility. Especially through the weighted average method to combine α ij and α ji , and allocate the weight according to the speed ratio, so that the risk assessment is more in line with the actual physical situation-the individual with high speed contributes more to the overall risk, so as to improve the rationality and accuracy of risk judgment.

[0055] 2. Compatible with static and dynamic obstacle scenarios, enhance system versatility. When the speed of a certain agent is zero (such as v j (t) = 0), the formula automatically degenerates into a static obstacle model that only depends on α ij , at this time β ij ≈ α ij , that is, equivalent to the traditional angle judgment method. Therefore, this scheme is not only suitable for multi-agent dynamic interaction, but also naturally covers the typical scenario of "agent-fixed obstacle". This feature enhances the versatility and compatibility of the system, enabling it to uniformly handle various obstacle avoidance problems in complex mixed environments (such as robot clusters coexisting with static facilities), reducing algorithm complexity and deployment difficulty.

[0056] 3. The collision risk is divided into three clear levels (high, low, and no), providing a clear logical basis for the design of subsequent control law.

[0057] Preferably, the control force direction function q ij (t) is: q ij (t) = h[l ij (t) + δ ij (t)];

[0058] Where δ ij (t) = Gl ij (t);

[0059] l ij = e ij / ||e ij (t)||;

[0060]

[0061] Vector l ij and vector δ ij are mutually orthogonal,

[0062] where h ∈ (0, 1) is a design coefficient, inversely proportional to the value of the critical distance Ω ij ; ||e ij (t) || is the distance between i and j; e ij (t) represents the relative position vector between agent i and agent j.

[0063] Such a setting, through the composite design of the principal direction and the orthogonal direction of the control force direction function, realizes the refinement and intelligence of the obstacle avoidance action, not only improves the safety and smoothness of the obstacle avoidance behavior, but also enhances the adaptability and control robustness of the system in complex dynamic environment.

[0064] Preferably, the switch function p ij (t) is:

[0065]

[0066] where, is a risk-free boundary parameter, indicating that there is a potential collision risk, triggering the anti-collision control.

[0067] Such a setting, through the logical design of the switch function based on the dynamic safety parameter, realizes the accurate triggering and efficient management of the anti-collision control, which not only guarantees the safety of the system, but also maintains the stability and operating efficiency of the collaborative control.

[0068] Preferably, the formation collaborative controller based on sliding mode control is:

[0069]

[0070] where g i is a control gain matrix, is a normal matrix, s i represents the modified sliding surface of the i-th agent; represents the direct online estimation value of the distributed observer to the unmatched uncertainty w of the i-th agent; represents the estimation value of the matching uncertainty d of the i-th agent; λ i is a normal number; δ vi represents the speed uncertainty estimation error or disturbance compensation term of the i-th agent; δ xirepresents the state uncertainty estimation error or disturbance compensation term of the i-th agent; x di represents the desired reference state vector of the i-th agent, including position and velocity.

[0071] Such a setting, 1. Realize the double compensation of mismatched and matched uncertainty, improve the robustness of the system. Traditional sliding mode control can usually only deal with matched uncertainty (i.e. The part that can be directly offset by the feedback term), and this scheme introduces and Estimate and compensate for mismatched uncertainty w and matched uncertainty d, respectively, to achieve comprehensive coverage of the two types of uncertainty. In particular Real-time online estimation by distributed observer, can effectively deal with model mismatch, external disturbance and other nonlinear disturbances, significantly enhance the adaptability and anti-interference performance of the system in unknown dynamic environment.

[0072] 2. Introduce multiple disturbance compensation terms to suppress the cumulative effect of estimation error. In addition to the main uncertainty estimation, the controller also contains δ vi and δ xi Two items, respectively, to compensate for residual errors or unmodeled disturbances in the state estimation process. This shows that the design not only depends on the estimated value itself, but also actively considers the influence of estimation bias. This "estimation + compensation" double-layer structure helps to prevent control drift or divergence caused by observation error accumulation, improving the stability and long-term reliability of the closed-loop system.

[0073] 3. Based on the modified sliding surface design, optimize the convergence performance and dynamic response. The controller takes the modified sliding surface s i As the core input variable, rather than the original error signal, indicating that it uses an improved sliding mode structure. The modified sliding surface usually combines error and its derivative information, and may introduce integral terms or filtering mechanisms, thereby improving the dynamic response characteristics of the system. For example, it can reduce chattering, speed up convergence, and improve tracking accuracy of the desired trajectory, especially suitable for task scenarios that require high-precision formation keeping.

[0074] Preferably, the modified sliding surface s i Of the i-th agent is:

[0075]

[0076] In the formula, e vi Is the speed tracking error vector of agent i, representing the deviation between the actual speed v i And the desired reference speed v di Of agent i; λ i Is a normal number; e xie is the compensation value of the unmatched uncertainty w estimated by the observer for the i-th agent; is the comprehensive vector of the entire network system uncertainty state.

[0077] Such settings, 1. Realize the multi-dimensional fusion of error information, improve the response accuracy and stability of sliding mode control. Traditional sliding mode control usually only constructs sliding surface based on position or speed error, while this method realizes the full order information fusion of motion state error by introducing the joint expression of e v and e xi This design makes the sliding surface not only reflect the current position deviation, but also contain the dynamic trend of the speed level, so as to more accurately capture the transient behavior of the system. Especially in formation control, the coordinated adjustment of position and speed is crucial, and this structure helps to achieve the dual goal of "position tracking + speed synchronization", significantly improving the overall collaborative performance.

[0078] 2. Introduce uncertainty compensation term Enhance the anti-interference ability of sliding surface. By embedding the compensation value of unmatched uncertainty estimated by the distributed observer Directly into the sliding surface construction, this scheme makes the sliding surface have the feedforward perception ability to unknown disturbance. This means that even if there is model mismatch or external disturbance, the sliding surface can still maintain good convergence characteristics, avoiding the sliding surface drift or divergence caused by uncertainty. This mechanism is equivalent to introducing "disturbance prediction" in sliding mode control, improving the robustness and adaptability of the controller in complex environment.

[0079] Preferably, in S3, I is designed as follows:

[0080]

[0081] In the formula, N msg (t) represents the number of information received per unit time; priority k (t) is the priority of the kth information source, priority k (t)∈(0~1); ω k is a fixed weight, reflecting the preset importance of different sources;

[0082] H is designed as follows:

[0083]

[0084] Where size z represents the equivalent size of the obstacle z; d safeis a safety distance threshold; v obs is the average moving speed of obstacles; v self is the self-motion speed;

[0085] The design of W is as follows:

[0086]

[0087] where N feedback (t) represents the number of feedbacks accepted per unit time; is the signal strength of the kth feedback; is the maximum allowed feedback strength; and λ is the quantity saturation parameter.

[0088] Such a setting, 1, the design of I introduces the information quantity N msg (t) and the priority of each information source priority k (t) and the fixed weight ω k , so that the system can not only perceive the total amount of information, but also can differentially filter and weight information according to the importance of the source and the real-time priority. For example, when a critical sensor fails, its priority can be dynamically reduced; while when a high-reliability node provides data, the weight can be increased. This mechanism avoids the noise interference caused by "information flood", enhances the selectivity and accuracy of information processing, and thus improves the robustness and reliability of the overall sensing system.

[0089] 2. The design of H comprehensively considers the geometric size (size z ), the spatial proximity (d safe ) and the relative motion state of the obstacle to form a nonlinear, dynamically changing danger index. Among them, the denominator emphasizes the high threat of close-range obstacles (square inverse relationship), while the speed ratio term reflects the potential risk of dynamic obstacles - even if the distance is far away, but the fast approaching one will be given a higher weight. This enables the system to identify and respond to high-speed moving obstacles in advance, significantly improving the forward-looking and safety of the obstacle avoidance strategy.

[0090] 3. The structure of W combines the two dimensions of feedback frequency and signal strength, and realizes nonlinear gain adjustment of feedback times through the exponential decay term , preventing control command oscillation or resource waste caused by frequent feedback. At the same time, the normalized sum of signal strengths ensures the quantitative consistency of feedback information, avoiding the dominance of single strong signal in decision-making. This design not only ensures the sensitive response to effective feedback, but also suppresses the influence of redundant or abnormal feedback, improving the stability and anti-disturbance ability of the control loop. BRIEF DESCRIPTION OF DRAWINGS

[0091] In order to make the purpose, technical scheme and advantages of the application clearer, the application will be further described in detail below with reference to the drawings, in which:

[0092] Figure 1 is a flowchart of the method;

[0093] Figure 2 is an example of the communication topology in Example 1;

[0094] Figure 3 is a schematic diagram of collision risk classification in Example 1;

[0095] Figure 4 is an action trajectory under the complete control rate in Example 2;

[0096] Figure 5 is an action trajectory without starting the interlayer information transmission control rate in Example 2;

[0097] Figure 6 is the system signal transmission amplitude in Example 2;

[0098] Figure 7 is the low-level intelligent agent reference tracking error in Example 2. DETAILED DESCRIPTION

[0099] The application will be further described in detail below through specific embodiments:

[0100] Example 1

[0101] As shown in the figure, the embodiment discloses a double-layer heterogeneous multi-agent system sliding mode formation control method, which comprises the following steps: Figure 1

[0102] S1, constructing a double-layer heterogeneous multi-agent system according to a preset form; the double-layer heterogeneous multi-agent system comprises two levels of high level and low level, the intelligent agents of each level comprise one leader and N followers, and the followers of the high level and the low level are one-to-one corresponding according to the index; wherein N≥1.

[0103] The dynamics of the system can be represented as:

[0104]

[0105] The dynamics of the follower i when m=1 (i.e. the high level) can be described as:

[0106]

[0107] The dynamics of the follower i when m=2 (i.e. the low level) can be described as:

[0108] ​

[0109] wherein, and denote the position vector and velocity vector of the i-th agent of the upper or lower layer respectively, is the coordinate of the agent in the global coordinate system, is the angle state of the agent, is the output vector of the formation position signal of the lower layer follower agent i. is the unmatched uncertainty, denotes the control gain matrix obtained by system modeling, is the control input, is the matched uncertainty. is a matrix of appropriate dimension, T is the terminal time, The above parameters satisfy the conditions of n1≥2, n2≥0, n3≥2, n≥2 and n1+n2=n.

[0110] Definition and Then the dynamics of the entire swarm is as follows:

[0111]

[0112] and has the following formula:

[0113]

[0114] It should be noted that in the double-layer heterogeneous multi-agent model proposed by the method, the upper layer (m=1) follows the first-order integral dynamics, and the lower layer (m=2) introduces and the uncertainty d i , w i to reflect its complexity, and the parameter constraints n1≥2, n3≥2 ensure the controllability of the motion.

[0115] S2, a cross-level hybrid communication topology structure is set for the double-layer heterogeneous multi-agent system; the cross-level hybrid communication topology structure comprises:

[0116] The upper layer agent can detect the information around the agent at the corresponding position of the lower layer or its adjacent agents;

[0117] Each upper layer follower transmits the environmental information obtained through perception detection to the upper layer leader; the upper layer leader obtains environmental information by comprehensively receiving information from each upper layer follower and through its own exploration;

[0118] The upper layer follower can directly transmit the detected information to the corresponding lower layer follower to achieve rapid response;

[0119] The high-level leader transmits the comprehensive environment information to the low-level leader, and the low-level leader distributes the information to all low-level followers, ensuring the overall coordination of the formation.

[0120] For the sake of understanding, Figure 2 For a communication topology example of 3 followers per layer.

[0121] The high-level agent can detect information around the low-level corresponding position agent or its adjacent agents. If an obstacle signal appears, the signal can be transmitted in two ways: 1. For the corresponding position agent, the signal can be directly transmitted; 2. For the non-corresponding position agent, the high-level agent transmits the signal to the high-level leader, the high-level leader transmits the signal to the low-level leader, and the low-level leader transmits the obtained signal to the corresponding agent to start obstacle avoidance work.

[0122] The communication topology of the system is: G={R(G),A(G)}. Where R(G)={r m,1 ,r m,2 ,...,r m,n+1},m=1,2. represents the node set, A(G)=[a ij ] is the adjacency matrix. Define in-degree of node r i , the degree matrix of the graph can be represented as D(G)=diag{deg in (r1),deg in (r2),...,deg in (r n+1 )}. The Laplacian matrix of the graph can be defined as L=D(G)-A(G).

[0123] The adjacency matrix of the high-level and low-level inside can be obtained as

[0124]

[0125] The adjacency matrix of the high-level to the low-level is

[0126]

[0127] Since the signal transmission of the double-layer multi-agent system is one-way from the high-level to the low-level, the final adjacency matrix can be obtained as:

[0128]

[0129] It should be noted that the high-level follower and the low-level corresponding agent (A 12The direct information transmission between the i-th and j-th agents (i = j) can significantly reduce the delay and achieve a fast response to the obstacle signal; the non-corresponding agents ensure global information coverage and system coordination through the hierarchical forwarding mechanism.

[0130] The cross-level hybrid communication topology combines direct and hierarchical transmission, has the characteristics of low delay and global coverage, embodies the advantages of "centralized decision-making-distributed execution", and the upper triangular structure of the adjacency matrix ensures the unidirectionality of the signal. The diagonal elements of the adjacency matrix A realize the "one-to-one" instruction transmission, and the Laplacian matrix (L) provides the basis for consistency analysis.

[0131] S3, setting the system control rate u of the double-layer heterogeneous multi-agent system i (t) = u 1,i (t) + u 2,i (t); wherein u 1,i (t) is the high-level control rate, u 2,i (t) is the low-level control rate;

[0132] High-level control rate

[0133] In the formula, I(t) represents the amount of perception information about the low-level environment received by the high-level leader from its corresponding high-level follower; H(t) represents the obstacle signal strength detected by the high-level leader itself; W(t) represents the feedback information strength or quantity reflecting the low-level formation coordination state and control demand received by the high-level leader from the low-level leader; k1(t), k2(t), k3(t) are weight coefficients; is the high-level collision avoidance control rate;

[0134] In specific implementation, the design of I is as follows:

[0135]

[0136] In the formula, N msg (t) represents the number of information received per unit time; priority k (t) is the priority of the kth information source, priority k (t) ∈ (0 ~ 1); ω k is a fixed weight, reflecting the preset importance of different sources.

[0137] The design of I introduces the logarithmic transformation of the number of information N msg (t), the priority priority k (t) of each information source, and the fixed weight ω kThis allows the system to not only perceive the total amount of information but also to selectively filter and weight information based on the importance and real-time priority of its source. For example, when a critical sensor fails, its priority can be dynamically reduced; while when data is provided by a high-reliability node, its weight can be increased. This mechanism avoids noise interference caused by the "information deluge," enhances the selectivity and accuracy of information processing, and thus improves the robustness and reliability of the overall perception system.

[0138] H is designed as follows:

[0139]

[0140] Where, size z d represents the equivalent size of obstacle z; safe The safe distance threshold; v obs v is the average moving speed of the obstacle. self For its own speed of movement.

[0141] The design of H takes into account the geometry (size) of the obstacle. z ), spatial proximity (d safe and relative motion state This forms a non-linear, dynamically changing risk index. The denominator... The system emphasizes the high threat level of nearby obstacles (inverse quadratic relationship), while the speed ratio reflects the potential risk of dynamic obstacles—even those that are far away but approach rapidly are given higher weight. This allows the system to identify and respond to high-speed moving obstacles in advance, significantly improving the foresight and safety of the obstacle avoidance strategy.

[0142] The design of W is as follows:

[0143]

[0144] Where, N feedback (t) represents the number of feedback received per unit of time; Let K be the signal strength of the k-th feedback. λ represents the maximum allowable feedback intensity; λ is the quantity saturation parameter.

[0145] The structure of W combines the two dimensions of feedback frequency and signal strength, and uses an exponential decay term. This achieves nonlinear gain adjustment based on the number of feedback cycles, preventing control command oscillations or resource waste caused by frequent feedback. Simultaneously, the sum of normalized signal strengths... This design ensures the quantitative consistency of feedback information, preventing a single strong signal from dominating decision-making. It guarantees a sensitive response to effective feedback while suppressing the effects of redundant or abnormal feedback, thus improving the stability and noise immunity of the control loop.

[0146] The high-level control law integrates the information amount, obstacle strength and feedback to realize the "decision-execution-feedback" closed loop. This multi-dimensional integration not only ensures the processing of high-priority tasks, but also dynamically quantifies the risk, providing a comprehensive decision basis for cross-layer collaboration.

[0147] In specific implementation, the low-level collision avoidance control rate

[0148] In the formula, is the low-level collision avoidance control rate; is a formation collaborative controller based on sliding mode control, used to ensure the relative position stability and trajectory tracking consistency between low-level agents.

[0149] In specific implementation, the low-level collision avoidance control rate is:

[0150]

[0151] In the formula, k ij is a weight coefficient; p ij (t) is a switching function; r ij (t) is a control force strength function; q ij (t) is a control force direction function.

[0152] The high-level collision avoidance strategy adopts the same collision avoidance control rate as the low-level agent, and the high-level collision avoidance control rate is:

[0153]

[0154] In the formula, the control force strength function r ij (t) is:

[0155]

[0156] In the formula, Ω ij is the critical distance, when ||e ij (t)||< Ω ij , it is considered that the agent i and j have entered the collision risk area; is the risk-free boundary parameter; ξ is a preset index, used to emphasize the influence degree of distance on the control force; β ij is the collision risk angle of the agent i and j.

[0157] In specific implementation, the risk-free boundary parameter may be a function related to β ij , for example:

[0158]

[0159] In the formula, m is a proportional coefficient.

[0160] If β ij is small (high risk), then is large -> even if the two agents are still far apart, the obstacle avoidance is triggered in advance;

[0161] If β ij is close to 90° (low risk), then is small -> the obstacle avoidance is triggered only when the distance is very close;

[0162] If β ij ≥ 90°: directly judged as no risk, and no obstacle avoidance force is applied.

[0163] In specific implementation, a critical value Ω ij is given for the collision risk between follower i and j ij , and a critical value Δ ij for the collision, i.e., when the distance ||e ij (t)|| < Ω ij , it is considered to enter the collision risk area, and when ||e ij (t)|| < Δ

[0164] In this way, the control force strength is designed to be proportional to the inverse power of the relative distance, and a sigmoid function is introduced for smooth modulation. When the distance between agents decreases, the control force increases rapidly in a non-linear manner, especially when it approaches the critical distance Ω ij , which rapidly rises, thereby realizing the "the closer the stronger" obstacle avoidance response mechanism. Compared with linear or step-type control force design, this non-linear structure can more realistically simulate the "sense of urgency" in human driving or biological obstacle avoidance behavior, effectively preventing collision accidents caused by slow response, and significantly improving the safety margin of the system. In addition, the collision risk angle β ij is introduced for segmented control, realizing directional obstacle avoidance priority judgment. The control force strength not only depends on the distance, but also is segmented according to the collision risk angle β ij : when β ij ≥ π / 2 (i.e., the relative motion direction is perpendicular or away), even if the distance is close, the strong control force is not triggered; and when β ij < π / 2 (i.e., there is a head-on or lateral approaching trend), the control strength is dynamically adjusted according to the distance. This mechanism embodies the "directional awareness" of obstacle avoidance logic, avoiding the same strength response to all close contacts, thereby reducing unnecessary control disturbance and improving the intelligence and rationality of the obstacle avoidance strategy. Moreover, by using the sigmoid function to adjust the risk difference By mapping the control force, it doesn't abruptly increase when entering the danger zone, but rather rises smoothly. This helps avoid drastic oscillations in the control signal, reduces actuator load, and ensures the stability of the closed-loop system. Furthermore, this design makes the control law mathematically differentiable, facilitating subsequent coupling with higher-order controllers such as sliding mode control, thus improving the convergence and robustness of the overall control performance.

[0165] In practical implementation, the collision risk angle β between agents i and j ij The formula for calculation is:

[0166]

[0167] In the formula, v i (t) and v j (t) represent the motion velocities of agents i and j, respectively, when v j When (t) = 0, it can be considered as a fixed obstacle; α ij Let α be the collision risk angle of agent i relative to agent j, defined as the angle between the direction of movement of agent i and the straight line from agent i to agent j, and stipulated that 0 ≤ α. ij ≤π;α ji Let be the collision risk angle of agent j relative to agent i; the different collision risk angles of agent i relative to agent j are as follows: Figure 3 As shown.

[0168] Based on collision risk angle β ij The size of the collision risk level between agents i and j is divided into the following three levels:

[0169] if There is a high risk of collision between agents i and j;

[0170] if There is a low risk of collision between agents i and j;

[0171] if There is no risk of collision between agents i and j.

[0172] Traditional methods often rely solely on relative position to determine proximity, neglecting the influence of relative motion direction, which can easily lead to misjudgments (e.g., a situation that is far away but close is mistakenly considered dangerous). This method introduces a collision risk angle β. ij This method comprehensively considers the relationship between the velocity magnitudes and directions of the two agents, achieving a dynamic and geometrical assessment of collision probability. Specifically, it combines a weighted average with α... ij With α jiand the weights are proportionally assigned according to the speed, so that the risk assessment is more in line with the actual physical situation - individuals with high speed contribute more to the overall risk, thereby improving the rationality and accuracy of risk judgment. In addition, when the speed of an agent is zero (such as v j (t) = 0), the formula automatically degenerates into a static obstacle model that only depends on a ij , that is, b ij ≈ a ij , which is equivalent to the traditional angle judgment method. Therefore, this scheme is not only suitable for multi-agent dynamic interaction, but also naturally covers the typical scenario of "agent - fixed obstacle". This feature enhances the universality and compatibility of the system, enabling it to uniformly handle various obstacle avoidance problems in complex mixed environments (such as robot clusters coexisting with static facilities), reducing algorithm complexity and deployment difficulty.

[0173] In implementation, the control force direction function q ij (t) is: q ij (t) = h[l ij (t) + d ij (t)];

[0174] Where d ij (t) = G l ij (t);

[0175] l ij = e ij / ||e ij (t)||;

[0176]

[0177] The vector l ij and the vector d ij are orthogonal to each other,

[0178] In the formula, h e (0, 1) is a design coefficient, which is inversely proportional to the value of the critical distance W ij ; ||e ij (t)|| is the distance between i and j; e ij (t) represents the relative position vector between agent i and agent j.

[0179] By composite design of the control force direction function in the principal direction and the orthogonal direction, the refinement and intelligence of the obstacle avoidance action are realized, which not only improves the safety and smoothness of the obstacle avoidance behavior, but also enhances the adaptability and control robustness of the system in complex dynamic environments.

[0180] The switching function p ij (t) is:

[0181]

[0182] wherein, is a risk-free boundary parameter, indicates a potential collision risk, triggering the collision avoidance control.

[0183] In specific implementation,

[0184] By logically designing the switching function based on the dynamic safety parameter, the precise triggering and efficient management of the collision avoidance control are realized, which not only guarantees the safety of the system, but also maintains the stability and operating efficiency of the cooperative control.

[0185] In specific implementation, the formation cooperative controller based on the sliding mode control is:

[0186]

[0187] wherein, g i is a control gain matrix, is a normal number matrix, s i represents the modified sliding surface of the i-th agent; represents the direct online estimation value of the distributed observer to the unmatched uncertainty w of the i-th agent; represents the estimation value of the matched uncertainty d of the i-th agent; λ i is a normal number; δ vi represents the speed uncertainty estimation error or disturbance compensation term of the i-th agent; δ xi represents the state uncertainty estimation error or disturbance compensation term of the i-th agent; x di represents the expected reference state vector of the i-th agent, including position and speed.

[0188] Traditional sliding mode control can usually only deal with matched uncertainty (i.e. the part that can be directly offset by the feedback term), while the present scheme introduces and to estimate and compensate for the unmatched uncertainty w and the matched uncertainty d, respectively, realizing comprehensive coverage of the two types of uncertainty. In particular estimated by the distributed observer in real time online, can effectively deal with nonlinear disturbances such as model mismatch and external disturbance, significantly enhancing the adaptability and anti-interference performance of the system in unknown dynamic environments. In addition to the main uncertainty estimation, the controller also contains δ vi and δ xiTwo terms are used to compensate for residual errors or unmodeled disturbances in the speed and state estimation processes. This indicates that the design not only relies on the estimated values themselves, but also actively considers the effects of estimation bias. This "estimation + compensation" two-layer structure helps prevent control drift or divergence caused by the accumulation of observation errors, improving the stability and long-term reliability of the closed-loop system. In addition, the controller uses a modified sliding surface s i as the core input variable, rather than the original error signal, indicating that it uses an improved sliding mode structure. The modified sliding surface usually combines error and its derivative information, and may introduce an integral term or filtering mechanism, thereby improving the dynamic response characteristics of the system. For example, it can reduce chattering, speed up convergence, and improve tracking accuracy of the desired trajectory, especially suitable for task scenarios that require high-precision formation keeping.

[0189] In specific implementation, the modified sliding surface s i of the i-th agent is:

[0190]

[0191] where e vi is the speed tracking error vector of agent i, representing the deviation between the actual speed v i of agent i and its expected reference speed v di ; λ i is a normal number; e xi is the position error of agent i, representing the deviation between the actual position of agent i and its expected reference position; is the compensation value of the unmatched uncertainty w acting on the i-th agent estimated by the observer; is the comprehensive vector of the entire network system uncertainty state.

[0192] Traditional sliding mode control usually constructs a sliding surface based only on position or speed error, while this method realizes full-order information fusion of motion state error by introducing the joint expression of e v and e xi . This design makes the sliding surface not only reflect the current position deviation, but also contain the dynamic trend at the speed level, so as to more accurately capture the transient behavior of the system. Especially in formation control, the coordinated adjustment of position and speed is crucial, and this structure helps achieve the dual goals of "position tracking + speed synchronization", significantly improving the overall collaborative performance. In addition, by compensating for the unmatched uncertainty estimated by the distributed observer Directly embedded into the sliding surface structure, this scheme enables the sliding surface to have the feedforward perception ability to unknown disturbances. This means that even if there is model mismatch or external disturbance, the sliding surface can still maintain good convergence characteristics, avoiding sliding surface drift or divergence caused by uncertainty. This mechanism is equivalent to introducing "disturbance prediction" in sliding mode control, improving the robustness and adaptability of the controller in complex environments.

[0193] For better understanding, the design process of the formation cooperative controller based on sliding mode control in the present method is described as follows.

[0194] The sliding mode group controller designed in the present method aims to ensure that the reference tracking error of the multi-agent system can be cooperatively consistent and ultimately remain bounded. To this end, the method of sliding mode control will be used for controller design, and the specific design steps are as follows.

[0195] Definition 1: For a network system with the state and reference state of the i-th node being x i (t) and x di (t), if there exists a closed set positive scalar b c and time t c (x i (t0), x di (t0), b c ) such that for all t≥t0+t c , i∈[1,N], and ||x i (t0)-x di (t0)||∈Ω, there is ||x i (t)-x di (t)||≤b c , then the state of the network system is called cooperatively consistently ultimately bounded.

[0196] Lemma 1: Consider a reference tracking network system containing N nodes, the reference tracking error state of the i-th node can be represented as e i (t)=x i (t)-x di (t), where e i (t)∈Ω and If we can find a positive definite function V satisfying V>0 when and V=0 if and only if and there exists a positive bounded number Φ such that when then the error state of the system is called cooperatively consistently ultimately bounded.

[0197] For both matching uncertainty and mismatching uncertainty, they can be represented as The reference tracking error of the ith agent can be defined as:

[0198]

[0199] The reference tracking error dynamics of the multi-agent system can be obtained as:

[0200]

[0201] where

[0202] Consider a dynamic system whose state-space equation is:

[0203]

[0204] where x is the system state vector, u is the control input, and are system matrices.

[0205] Selection of the sliding surface s(x):

[0206]

[0207] where and are design parameters, s(x) is the sliding surface function, and it is usually desired that the system state slides on the surface s(x) = 0.

[0208] Design of the sliding mode controller u:

[0209] To make the system state slide on the sliding surface, the controller is chosen as follows:

[0210] u = u eq - Ksgn(s(x));

[0211] where u eq is the equivalent control term; K is the control gain; sgn(s(x)) is the sign function, which provides the positive and negative direction information for the sliding surface s(x). And here

[0212] Then to guarantee the existence of sliding motion for unmatched uncertainties, the modified sliding surface of the ith agent is defined as:

[0213]

[0214] Here λ i is a positive constant, which is equivalent to e xi is equivalent to x, is equivalent to and is the local deformation and velocity tracking error vector, represents the local mismatched uncertain observation of the ith agent and is the local mismatched uncertain observation of the ith agent and adding design parameters to ensure the existence of sliding motion of mismatched uncertainty.

[0215] Therefore, define S = [s1 T ,s2 T ,…,s N T ] T , the time derivative of the modified sliding variable is obtained by the following formula:

[0216]

[0217] where Λ = diag{λ1, λ2, …, λ N}; B = diag{b1, b2, …, b N}, b i is a normal number; is the estimated value of the system matching uncertainty d.

[0218] Finally, the sliding mode group controller based on the distributed observer can be designed as:

[0219]

[0220] where and

[0221] Combined with

[0222] The final control rate of the low layer can be obtained as:

[0223]

[0224] Finally, according to the high-level control rate and the low-level control rate, the final control rate can be obtained as follows:

[0225]

[0226] S4, based on the constructed double-layer heterogeneous multi-agent system, using the system control rate of S3, the formation control and obstacle avoidance collaborative operation of the multi-agent system are carried out, and the collaborative consistency of the reference tracking error and the real-time prevention and control of the collision risk are ensured under the condition of the existence of mismatched uncertainty.

[0227] The method proposes a heterogeneous multi-agent system structure containing two levels of high and low layers, each layer is provided with a leader and N followers, and the followers of the high and low layers are one-to-one corresponding. This structure separates global decision-making and local execution: high-level agents are responsible for perceiving the environment, integrating information and making macro decisions; low-level agents focus on path tracking and obstacle avoidance and other specific operations. Compared with traditional single-layer or multi-homogeneous agent systems, this two-layer structure significantly improves the scalability and task processing efficiency of the system. Especially in large-scale group tasks, it avoids the communication overhead and computing bottleneck caused by direct communication of all agents, realizes the optimization mode of "centralized decision-making and distributed execution", and enhances the organization and controllability of the system. In addition, the scheme introduces a cross-level hybrid communication topology, including: high-level agents can detect the environmental information of the corresponding position or adjacent agents of the bottom layer; high-level followers upload the perceived information to the high-level leader; the high-level leader transfers the instructions to the low-level leader after integrating the environmental information; the low-level leader distributes the instructions to each low-level follower; at the same time, the high-level follower can also directly transmit information to the corresponding low-level follower to achieve rapid response. This hybrid communication mechanism breaks through the limitations of the traditional single uplink and downlink communication mode, ensuring the aggregation and coordination of global information, while retaining the ability of local rapid response. Compared with the existing communication mode which only relies on the center node or fixed topology, this structure effectively alleviates the information delay problem and improves the adaptability and cooperation efficiency of the system in dynamic environments.

[0228] Moreover, the method proposes to decompose the system control rate into high-level control rate u 1,i (t) and low-level control rate u 2,i (t). The high-level control rate is composed of environmental perception information I(t), obstacle signal strength H(t), formation feedback information W(t) and anti-collision term , realizing a "decision-making-execution-feedback" closed loop. This multi-dimensional integration not only ensures the processing of high-priority tasks, but also dynamically quantifies the risk, providing a comprehensive decision basis for cross-layer cooperation. The low-level control rate is composed of anti-collision control term and a cooperative controller based on sliding mode control The design realizes the closed-loop control logic of "high-level decision driving + low-level sliding mode execution". Compared with the traditional method of using sliding mode control only at the low level, this scheme embeds sliding mode control into the entire hierarchical system and optimizes it jointly with the anti-collision logic, not only enhancing the robustness of the system to uncertainties, but also improving the overall control accuracy and safety. In addition, this method integrates the anti-collision control item into the high-level and low-level control law, so that the formation control and collision risk prevention are synchronized. The high-level leader can consider the obstacle distribution and formation state when making decisions, and generate safe instructions in advance; the low-level agent can also respond to local threats in real time during execution, thereby avoiding trajectory mutations or formation ruptures caused by passive obstacle avoidance. Compared with existing methods that handle formation control and obstacle avoidance independently (such as completing formation first and then triggering obstacle avoidance), this scheme realizes integrated design of the two, reducing control conflicts and response delays, and improving the overall performance of the system in complex dynamic environments.

[0229] This method effectively solves the deficiencies of traditional multi-agent systems in information transmission efficiency, control robustness, and safety coordination by constructing a double-layer heterogeneous architecture, designing a hybrid communication topology, introducing a hierarchical sliding mode control law, and integrating an anti-collision mechanism. It not only improves the stability and adaptability of the system in the face of model uncertainties, external disturbances, and communication mismatches, but also realizes the unified optimization of formation consistency and collision risk prevention.

[0230] Embodiment Two

[0231] To better illustrate the effect of this method, the following example is given.

[0232] In the time-varying mode, real-time research is conducted on two examples, and the transmission signal capability of the control law used by the system, the obstacle avoidance success rate, and the reference tracking error are also studied.

[0233] In the double-layer leader-follower mobile multi-agent system, let n i = 4, T = 10 s. Assume that the multi-agent system with 8 follower agents (4 high-level agents and 4 low-level agents) moves in a fixed sinusoidal trajectory, then we conduct simulation experiments from three aspects: using the complete control law, using only the low-level control law, and not using the control law.

[0234] A. Formation action trajectory under the use of complete control law

[0235] In the design of the high-level agent control law, set k1 = 1, k2 = 0.5, k3 = 0.3, and set the control parameter ω of the key area to 1.0, while the ω of the ordinary area is 0.5. The safety distance d safeThe sliding mode control parameter λ is set to 1. Under the overall framework of high-level and low-level collaborative control, the system exhibits excellent formation and obstacle avoidance performance.

[0236] The high-level agent synchronizes the obstacle information to all low-level agents by direct signal transmission and cooperation with the low-level agents. As shown in Figure 4 The high-level agent ensures that the low-level agents generate a repulsive force field around the obstacle while maintaining its own trajectory, achieving smooth avoidance behavior in path planning and avoiding any collision. The anti-collision control rate calculates the collision risk level (low / medium / high risk) in real time according to the obstacle distance, and when the agent enters the high-risk area, the control force amplitude is increased and the direction function adjusts the heading angle deviation to the safety threshold, effectively improving the robustness of the system. The existence of the high-level agent not only enhances the efficiency of information transmission, but also provides more accurate obstacle avoidance guidance for the low-level agents.

[0237] B. Formation trajectory without starting inter-layer information transmission control rate

[0238] Set k ij = 1, m = 1, α = 2. According to the simulation results Figure 5 ), after turning off the high-level control rate, the system relies only on low-level anti-collision and sliding mode control, and the overall performance degrades. At this time, the low-level agent cannot obtain the global obstacle information provided by the high-level agent, and can only rely on its own local perception for obstacle avoidance. Due to the lack of global vision support from the high-level agent, the agent located at the edge of the formation cannot respond to the second obstacle in time when facing obstacles due to information lag, resulting in a single collision. This information lag makes it difficult for low-level agents to make effective path planning and obstacle avoidance decisions in complex environments, significantly reducing the robustness and safety of the system. In addition, the lack of cooperation of the high-level agent limits the reaction speed and accuracy of the low-level agent when responding to dynamic environmental changes, further affecting the overall coordination and stability of the formation. This shows that the high-level agent plays a crucial role in the multi-agent system, and the global information and collaborative control ability it provides are essential for the efficient operation and safety of the system.

[0239] C. Transmission signal capacity, obstacle avoidance success rate and reference tracking error of the system

[0240] As Figure 6As shown in the simulation experiment, the high-level agent reflects the integration of multiple signals and its real-time response to the system state. The high-level agent obtains a comprehensive decision signal by weighting and fusing the information quantity signal, obstacle signal and feedback signal. This signal not only indicates the multiple influences on the system in the current environment, but also provides clear guidance for the action of the low-level agent. The low-level agent generates a corresponding response according to the control rate transmitted by the high-level, and then through the feedback signal, the high-level agent can adjust its decision strategy at the next moment, thereby realizing the adaptive regulation and robustness enhancement of the entire platform.

[0241] Then the two states of the low-level agent in the obstacle avoidance process are compared, and the table is used to intuitively show the collision avoidance success rate of the active obstacle avoidance area and the obstacle avoidance cancellation area. As shown in Table 1, the experimental data shows that the obstacle avoidance success rate using the complete control rate is about 95.9%, and the obstacle avoidance success rate using only the low-level control rate is 88.4%.

[0242] Table 1 Comparison of collision avoidance success rate with and without high-level information transmission control rate

[0243]

[0244] This result fully embodies the guiding role of the high-level agent on the low-level agent through the information transmission control rate, that is, after integrating state error, disturbance signal and other multiple information, the high-level agent adjusts the control command in real time, so that the low-level agent can still maintain high response accuracy and robustness in the face of active obstacle avoidance, further verifying the advantage and necessity of the high-level information transmission control rate in the coordination of multi-agent systems.

[0245] As Figure 7 shown in the reference tracking error versus time graph, the blue solid line represents the mean value of the reference tracking error of all low-level agents in the entire simulation process, and the red dashed line shows the fluctuation range of one standard deviation above and below the mean value. From Figure 7 , it can be seen that in the initial stage, the tracking error is high due to the influence of state deviation and external disturbance; but under the rapid adjustment of the sliding mode group control strategy, the error rapidly decreases in about 2-3 seconds, and remains stable in the subsequent time. Specifically, when the system enters the steady state, the mean value of the tracking error stabilizes at a low level of about 0.08-0.1, and the standard deviation maintains in a narrow interval of about 0.01-0.02. This result fully embodies the advantage of using sliding mode group control: even in a complex environment with obstacle avoidance disturbance and random disturbance, the control strategy can still make the low-level agent rapidly and accurately approach the desired trajectory, thereby showing excellent robustness and coordination effect.

[0246] Table 2 Anti-collision success rate of different collision risk classification methods

[0247]

[0248] In the simulation results, the anti-collision success rates under the old classification method are 83.41%, 83.85%, 93.65%, and 100.00% in turn. Using simple arithmetic mean, the overall anti-collision success rate is 90.23%. Considering that the span of each angle interval is different, among which 0-30°, 30-60°, and 60-90° are each 30°, and 90-180° is 90°, if the interval angle is used as the weight, the weighted average anti-collision success rate is 93.48%. In contrast, the anti-collision success rates under the new classification method are 87.73%, 79.39%, and 100% in turn. The arithmetic mean is 89.04%, and according to 0-45° and 45-90° each 45°, 90-180° is 90°, the weighted average anti-collision success rate is 91.78%.

[0249] Although the average success rate of the second method is slightly lower than that of the first method whether it is arithmetic mean or weighted mean, this difference is still within an acceptable range. More importantly, the second method is divided into only three intervals, making the risk division simpler and more intuitive, facilitating rapid judgment and optimization of anti-collision strategies in practical applications, and also more in line with the characteristics of actual collision risk distribution.

[0250] In summary, this simulation verifies the excellent performance of the system in obstacle avoidance, information transmission, and group control. High-level agents can quickly and accurately transmit key information to achieve timely response; the sliding mode group control exhibits excellent robustness, significantly improving overall stability; and although the success rate of the three types of collision risk assessment is slightly lower, the classification method is simple and intuitive, facilitating practical applications. Overall, the strategies work together to effectively improve the overall control rate of the system. That is, the effectiveness of the proposed formation control scheme is verified.

[0251] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and not to limit the technical solutions. Those of ordinary skill in the art should understand that modifications or equivalent replacements to the technical solutions of the present application without departing from the spirit and scope of the technical solutions should be covered in the scope of the claims of the present application.

Claims

1. A method for sliding mode formation control of a double-layer heterogeneous multi-agent system, characterized in that, Comprise the following steps: S1, according to the preset form to construct double layer heterogeneous multi-agent system;The double layer heterogeneous multi-agent system includes high and low two levels, the agent of each level includes 1 leader and N follower, and the follower between high and low layer is one-to-one corresponding according to index;Wherein, N≥1; S2, set up cross level mixed communication topology structure to double layer heterogeneous multi-agent system;The cross level mixed communication topology structure includes: High layer agent can detect the information around the corresponding position agent or its adjacent agent of low layer; Each high layer follower passes through the environmental information obtained by sensing detection to high layer leader;High layer leader obtains environmental information by itself exploration and receiving information from each high layer follower; High layer follower can directly pass the information detected to the corresponding low layer follower, realize fast response; High layer leader passes the comprehensive environmental information to low layer leader, and then distributes to all low layer followers by low layer leader, ensure the overall coordination of formation; S3, setting the system control rate u of the double-layer heterogeneous multi-agent system i (t) = u 1,i (t) + u 2,i (t); wherein u 1,i (t) is a high-level control rate, u 2,i (t) is a low-level control rate High-level control rate In the formula, I(t) represents the amount of perception information about the low-layer environment received by the high-layer leader from the corresponding high-layer follower; H(t) represents the obstacle signal strength detected by the high-layer leader itself; W(t) represents the feedback information strength or amount reflecting the low-layer formation coordination state and control demand received by the high-layer leader from the low-layer leader; k1(t), k2(t), and k3(t) are weight coefficients; Collision avoidance control rate of the high layer; Low layer control rate In the formula, is a low-level collision control rate; is a formation cooperative controller based on sliding mode control, used to ensure the consistency of relative position stability and trajectory tracking among low-level agents. S4, based on the constructed double layer heterogeneous multi-agent system, using the system control rate of S3, the formation control and obstacle avoidance collaborative operation of multi-agent system is carried out, ensure that the system realizes the collaborative consistency of reference tracking error and real-time prevention and control of collision risk under the condition of mismatch uncertainty. 2.The double-layer heterogeneous multi-agent system sliding mode formation control method of claim 1, wherein: In S3, the low-level collision avoidance control rate is: where k ij is a weighting factor; p ij (t) is a switching function; r ij (t) is a control force strength function; q ij (t) is a control force direction function. 3.The double-layer heterogeneous multi-agent system sliding mode formation control method of claim 2, wherein: In S3, the collision avoidance strategy of high layer uses the same collision avoidance control rate as low layer agent, and the collision avoidance control rate of high layer is: 4.The double-layer heterogeneous multi-agent system sliding mode formation control method of claim 2, wherein: Control force strength function r ij (t) is: where Ω ij is the critical distance, and when ij ij agents i and j are considered to enter the collision risk region; is the risk-free boundary parameter; ξ is a preset index used to emphasize the degree of influence of the distance on the control force.​ β ij is the collision risk angle for agents i and j.

5. The double-layer heterogeneous multi-agent system sliding mode formation control method of claim 4, wherein: Collision risk angle β of agents i and j ij The formula for this is: wherein v i (t) and v j (t) are the velocities of agents i and j, respectively, when v j (t) = 0, can be considered as a fixed obstacle; a ij is the collision risk angle of agent i with respect to agent j, defined as the angle between the moving direction of agent i and the straight line from agent i to agent j, and is specified as 0 < a ij ≤ π; a ji is the collision risk angle of agent j with respect to agent i. Based on the size of the collision risk angle β ij The collision risk level between agents i and j is classified into the following three levels: If then there is a high collision risk between agents i and j; If then there is a low collision risk between agents i and j; If then there is no collision risk between agents i and j.

6. The double-layer heterogeneous multi-agent system sliding mode formation control method of claim 4, wherein: Control force direction function q ij (t) is: q ij (t) = h[l ij (t) + δ ij (t)]; where δ ij (t) = G ij (t); l ij = e ij / ||e ij (t)||; Vector l ij and vector δ ij are mutually orthogonal, where h e (0, 1) is a design coefficient inversely proportional to the value of the critical distance Ω ij ; ||e ij (t)|| is the distance between i and j; e ij (t) represents the relative position vector between agent i and agent j.

7. The double-layer heterogeneous multi-agent system sliding mode formation control method of claim 4, wherein: Switching function p ij (t) is: In the formula, Indicates a potential collision risk, triggering collision avoidance control.

8. The double-layer heterogeneous multi-agent system sliding mode formation control method of claim 1, wherein: Formation cooperative controller based on sliding mode control For: where g i is a control gain matrix, is a constant matrix, s i denotes the modified sliding surface of the ith agent; denotes the direct online estimation of the mismatched uncertainty w of the ith agent by the distributed observer; denotes the estimation of the matched uncertainty d of the ith agent; λ i is a constant; δ vi denotes the velocity uncertainty estimation error or disturbance compensation term of the ith agent; δ xi denotes the state uncertainty estimation error or disturbance compensation term of the ith agent; x di denotes the desired reference state vector of the ith agent, including position and velocity.

9. The double-layer heterogeneous multi-agent system sliding mode formation control method of claim 8, wherein: The modified sliding surface s of the i-th agent i is: where e vi is the velocity tracking error vector of agent i, representing the deviation between the actual velocity v i of agent i and its desired reference velocity v di ; λ i is a positive constant; e xi is the position error of agent i, representing the deviation between the actual position of agent i and its desired reference position; is the compensation value of the unmatched uncertainty w acting on the i-th agent estimated by the observer; is the comprehensive vector of the entire network system uncertainty state.

10. The double-layer heterogeneous multi-agent system sliding-mode formation control method of claim 1, wherein: The design of I in S3 is as follows: where N msg (t) represents the number of information received per unit of time; priority k (t) is the priority of the kth information source, priority k (t) ∈ (0-1); ω k is a fixed weight, reflecting the preset importance of different sources; The design of H is as follows: wherein size z represents the equivalent size of the obstacle z; d safe is a safety distance threshold; v obs is the average moving speed of the obstacle; v self is the self-motion speed; The design of W is as follows: where N feedback (t) denotes the number of feedbacks accepted per unit time; is the signal strength of the kth feedback; is the maximum allowed feedback strength; and λ is the number saturation parameter.

Images